Q: What is the total or count of factors of the number 678,348?

 A: 48

How do I find the total factors of the number 678,348?

Step 1

Find the prime factorization of the number 678,348.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

Factor Tree
678,348
Factor Arrows
2339,174
Factor Arrows
2169,587
Factor Arrows
356,529
Factor Arrows
318,843
Factor Arrows
36,281
Factor Arrows
11571

The prime factorization in exponential form is: 22 x 33 x 111 x 5711

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

678,348 = 22 x 33 x 111 x 5711
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(678348) = (2 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(678348) = (3)(4)(2)(2)
Down Arrow
d(678348) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 678,348 and how to find them.

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